How to Find a Number of Terms in an Arithmetic Sequence

PDF download Download Article
PDF download Download Article

Finding the number of terms in an arithmetic sequence might sound like a complex task, but it’s actually pretty straightforward. All you need to do is plug the given values into the formula t n = a + (n - 1) d and solve for n , which is the number of terms. Note that t n is the last number in the sequence, a is the first term in the sequence, and d is the common difference.

Steps

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/5d\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-1-Version-2.jpg\/v4-460px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/5\/5d\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-1-Version-2.jpg\/aid4097368-v4-728px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Typically, to solve a problem like this, you’ll be given the first 3 or more terms as well as the last term. [1]
    • For example, you may have the following sequence: 107, 101, 95…-61. In this case, the first term is 107, the second term is 101, and the last term is -61. You need all of this information to solve the problem.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/00\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-2-Version-2.jpg\/v4-460px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-2-Version-2.jpg","bigUrl":"\/images\/thumb\/0\/00\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-2-Version-2.jpg\/aid4097368-v4-728px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    In the example sequence, the first term is 107 and the second term is 101. So, subtract 107 from 101, which is -6. Therefore, the common difference is -6. [2]
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/4e\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-3-Version-2.jpg\/v4-460px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-3-Version-2.jpg","bigUrl":"\/images\/thumb\/4\/4e\/Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-3-Version-2.jpg\/aid4097368-v4-728px-Find-a-Number-of-Terms-in-an-Arithmetic-Sequence-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Plug in the last term ( t n ), the first term ( a ), and the common difference ( d ). [3] Work through the equation until you’ve solved for n . [4]
    • For example, start by writing: -61 = 107 + (n - 1) -6. Subtract 107 from both sides so you’re left with -168 = (n - 1) -6. Then, divide both sides by -6 to get 28 = n - 1. Finish by adding 1 to both sides so that n = 29.
    4. Advertisement


Community Q&A

Search
Add New Question
  • Question
    Can I use the formula (A - L/d) + 1 for finding n?
    Donagan
    Top Answerer
    As explained above, n = [(L - A) / d] + 1.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 48 Helpful 72
  • Question
    If the difference is not given, how do I find the difference?
    Donagan
    Top Answerer
    Subtract any term from the one that follows it.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 66 Helpful 64
  • Question
    If the first term and last term of an arithmetic progression are 5 and 89, how do I find the number of terms?
    Donagan
    Top Answerer
    You can't without knowing the difference between consecutive terms.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 84 Helpful 101
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      • The difference between the last term and first term will always be divisible by the common difference.
        Thanks
      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Submit
      Thanks for submitting a tip for review!
      Advertisement

      Warnings

      Advertisement

      You Might Also Like

      How to
      Find Any Term of an Arithmetic Sequence
      How to
      Find the Sum of an Arithmetic Sequence
      How to
      Find the Maximum or Minimum Value of a Quadratic Function Easily
      How to
      Factor a Cubic Polynomial
      How to
      Solve a Cubic Equation
      How to
      Learn Algebra
      How to
      Solve for X
      How to
      Algebraically Find the Intersection of Two Lines
      Armor Class in D&D 5E: What Is It & How Can You Calculate It?
      How to
      Calculate Frequency
      How to Solve a Quadratic Equation: A Step-by-Step Guide
      How to
      Solve Systems of Algebraic Equations Containing Two Variables
      Your Guide to Flipping the Inequality Sign (And Solving Inequalities)
      How to Complete the Square to Solve a Quadratic Equation
      Advertisement

      References

      1. ↑ https://youtu.be/hGiuMNIR7Gk?t=13
      2. ↑ https://www.alamo.edu/contentassets/afe30946fa58450c89840c1173f3b9d0/sequences/math1314-arithmetic-sequences.pdf
      3. ↑ https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
      4. ↑ https://youtu.be/hGiuMNIR7Gk?t=59

      About This Article

      In other languages
      Thanks to all authors for creating a page that has been read 517,907 times.

      Reader Success Stories

      • Chinmay Sharma

        Jul 30, 2020

        "I always like wikiHow. It is awesome and can teach anything in a playful manner; all the best wikiHow team."
      More reader stories Hide reader stories
      Share your story

      Did this article help you?

      Advertisement